Question

Find the solution to the system of equations.
You can use the interactive graph below to find the solution.

\[\begin{cases}
y=x-4
\\\\
y=4x+2
\end{cases}\]
\[x= \]
\[y= \]

Answer 1

To solve the system of equations

\[
\begin{cases}
y = x - 4 \\
y = 4x + 2
\end{cases}
\]

we can set the equations equal to each other since both are equal to \( y \):

\[
x - 4 = 4x + 2
\]

Now, we will solve for \( x \):

1. Subtract \( x \) from both sides:

\[
-4 = 4x - x + 2
\]

\[
-4 = 3x + 2
\]

2. Subtract \( 2 \) from both sides:

\[
-4 - 2 = 3x
\]

\[
-6 = 3x
\]

3. Divide by \( 3 \):

\[
x = -2
\]

Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the first equation \( y = x - 4 \):

\[
y = -2 - 4
\]

\[
y = -6
\]

Thus, the solution to the system of equations is:

\[
x = -2
\]

\[
y = -6
\]

In conclusion, the solution is:

\[
x = -2, \, y = -6
\]